Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem

TL;DR

This paper derives asymptotic formulas for eigenvalues and eigenfunctions of a boundary-value problem with discontinuities and retarded arguments, incorporating spectral parameters in transmission conditions.

Contribution

It introduces novel asymptotic formulas for eigenvalues and eigenfunctions in a boundary-value problem with discontinuities and retarded arguments, including spectral parameters in transmission conditions.

Findings

Asymptotic formulas for eigenvalues derived

Asymptotic formulas for eigenfunctions derived

Applicable to boundary-value problems with discontinuities and retarded arguments

Abstract

In this work a discontinuous boundary-value problem with retarded argument which contains spectral parameter in the transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.